# From Boltzmann equations to steady wall velocities

## Abstract

By means of a relativistic microscopic approach we calculate the expansion velocity of bubbles generated during a first-order electroweak phase transition. In particular, we use the gradient expansion of the Kadanoff-Baym equations to set up the fluid system. This turns out to be equivalent to the one found in the semi-classical approach in the non-relativistic limit. Finally, by including hydrodynamic deflagration effects and solving the Higgs equations of motion in the fluid, we determine velocity and thickness of the bubble walls. Our findings are compared with phenomenological models of wall velocities. As illustrative examples, we apply these results to three theories providing first-order phase transitions with a particle content in the thermal plasma that resembles the Standard Model.

- Authors:

- DESY, Notkestr. 85, 22607 Hamburg (Germany)

- Publication Date:

- OSTI Identifier:
- 22375881

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BOLTZMANN EQUATION; EQUATIONS OF MOTION; HIGGS BOSONS; HIGGS MODEL; RELATIVISTIC RANGE; STANDARD MODEL; VELOCITY

### Citation Formats

```
Konstandin, Thomas, Nardini, Germano, and Rues, Ingo, E-mail: thomas.konstandin@desy.de, E-mail: germano.nardini@desy.de, E-mail: ingo.rues@desy.de.
```*From Boltzmann equations to steady wall velocities*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/09/028.

```
Konstandin, Thomas, Nardini, Germano, & Rues, Ingo, E-mail: thomas.konstandin@desy.de, E-mail: germano.nardini@desy.de, E-mail: ingo.rues@desy.de.
```*From Boltzmann equations to steady wall velocities*. United States. doi:10.1088/1475-7516/2014/09/028.

```
Konstandin, Thomas, Nardini, Germano, and Rues, Ingo, E-mail: thomas.konstandin@desy.de, E-mail: germano.nardini@desy.de, E-mail: ingo.rues@desy.de. Mon .
"From Boltzmann equations to steady wall velocities". United States.
doi:10.1088/1475-7516/2014/09/028.
```

```
@article{osti_22375881,
```

title = {From Boltzmann equations to steady wall velocities},

author = {Konstandin, Thomas and Nardini, Germano and Rues, Ingo, E-mail: thomas.konstandin@desy.de, E-mail: germano.nardini@desy.de, E-mail: ingo.rues@desy.de},

abstractNote = {By means of a relativistic microscopic approach we calculate the expansion velocity of bubbles generated during a first-order electroweak phase transition. In particular, we use the gradient expansion of the Kadanoff-Baym equations to set up the fluid system. This turns out to be equivalent to the one found in the semi-classical approach in the non-relativistic limit. Finally, by including hydrodynamic deflagration effects and solving the Higgs equations of motion in the fluid, we determine velocity and thickness of the bubble walls. Our findings are compared with phenomenological models of wall velocities. As illustrative examples, we apply these results to three theories providing first-order phase transitions with a particle content in the thermal plasma that resembles the Standard Model.},

doi = {10.1088/1475-7516/2014/09/028},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 09,

volume = 2014,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}